I think we should not confuse the initial power switch on sequence that will involve not only OS initialisation but screen initialisation and flash disk initialisation with the power down that happens after a screen is displayed. The relative slowness of the 256MB Flash memory may be partly to blame for the power switch on delay, the fact that Flash disk drives do a complete check for, and isolation of, faulty memory locations on power up. Also on the iLiad the whole OS is apparently on Flash because it can have its software upgraded by downloading a new version of the OS into the device.
When you switch the device on it almost immediately shows a screen that says iRex iLiad please wait... then there is a delay of about 30 seconds before the first, default, screen is displayed, only then is the file system, touch screen and WiFi active. Exactly the same procedure was followed on the Sony LIBRIe I tested last year.
However, after a screen is displayed the power light switches off almost immediately and only switches on again if you press one of the switches, or use the stylus. This must mean that it then simply runs a little software loop that just checks for key presses and touch screen input, whilst powering down everything else. The power light then stays on for little more than a second as the new screen is displayed.
When you switch the iLiad off using the on/off switch it goes through a screen clear procedure that tends to leave a ghost negative image of the last page viewed on the screen.
The touch screen can not be turned off.
Unfortunately have now had to return the device so can not test the maths notation capability, but iRex have promised me a full working version when the next batch is delivered to Eindhoven, this should allow me to test some of the features that I have so far been unable to examine.